The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#
Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
First, we will multiply each side of the equation by #color(red)(6)# to eliminate the fractions because by the definition above all of the coefficients and the constant must be integers:
#color(red)(6) * y = color(red)(6)(-3/2x + 4/3)#
#6y = (color(red)(6) xx -3/2x) + (color(red)(6) xx 4/3)#
#6y = (cancel(color(red)(6))3 xx -3/color(red)(cancel(color(black)(2)))x) + (cancel(color(red)(6))2 xx 4/color(red)(cancel(color(black)(3))))#
#6y = -9x + 8#
Now, we will add #color(red)(9x)# to each side of the equation to put this equation into standard form:
#color(red)(9x) + 6y = color(red)(9x) - 9x + 8#
#9x + 6y = 0 + 8#
#color(red)(9)x + color(blue)(6)y = color(green)(8)#
